Superconducting systems employing superconducting cables and coils, especially cable-in-conduit cables (CCIC), are used in nuclear fusion experiments and superconducting magnet energy storage (SMES).
The interest is to design cables, which can also be fashioned into coils, to carry as large a current as possible. For example, the magnetic field from an electromagnet is a function of the current flowing in its coil.
Generally, the smaller the resistance in a conductor, the larger is its current capacity. Resistance can be reduced by having a conductor with a larger cross-section, and also by being in a superconducting state. However, at high frequencies, current tends to flow near the surface of a conductor and therefore the inner core is not utilized. Also, a thick solid conductor or cable is not easy to bend and is susceptible to breakage. Thus, it has been a standard design to use stranded cable of equivalent cross-section in place of a single solid cable. In fact superconducting systems have been built using individually insulated superconducting strands because of the above-mentioned considerations.
However, the insulated strands tend to carry the current unevenly under superconducting conditions in a phenomenon now identified as "strand channeling". This results in the current in some strands reaching the critical current much earlier than others so that quenching occurs prematurely. Thus a CCIC magnet is found to be quenched at a current much lower than its design value. In recent CICC magnets, the strands are not completely insulated, but their surfaces are coated by highly resistive material such as chromium. This allows some degree of current redistribution or shunting among strands.
FIG. 1 shows an example of a cross section of a conventional cable-in-conduit cable (CICC), referred to as "a CIC cable". In the cable-in-conduit cable shown in FIG. 1, several tens to several hundred superconducting strands are packed into a stainless-steel conduit (tubular structure).
The void ratio of a cable-in-conduit cable, which expresses the proportion of a cross section less the surface area of the strands, is commonly believed to be about 35 to 37%. (See, for example, Takahashi et al., "Effect of Chrome Plating on Connection Loss of Cable-in-Conduit Cable," Collected Preprints of 52.sup.nd Meeting of Low-Temperature Engineering/Superconductivity Society, Fall of 1994 [Dai-52-kai, 1994 Nendo Shuki Teion Kogaku/Chodendo Gakkai Yokoshu], A3-6, p. 225
Electric current in a superconducting state is passed through such strands by cooling them to below the critical temperature using coolant such as liquid helium or supercritical helium. A conduit forms a helium channel in addition to functioning as a support against the enormous electromagnetic forces exerted on the cable.
FIG. 2 shows an example of a method for manufacturing such a CIC cable. In FIG. 2, the strand has a diameter of 0.76 mm and contains in its central portion embedded superconducting filaments consisting of copper and NbTi, Nb.sub.3 Sn, or the like. In the example, three strands are twisted into a single stranded wire, three such stranded wires are twisted into a single stranded wire, these operations are performed two more times, and six cables are finally placed in a conduit measuring 23.0.times.27.6 mm. Ultimately, 3.times.3.times.3.times.3.times.6=486 strands are used in the example shown in FIG. 2.
Several reasons exist for using a multitude of stranded wires. One reason is to reduce the AC loss. An eddy current flows near the conductor surface of an alternating-current circuit or a conductor in a magnetic field that varies over time. (This effect is called "the skin effect.") As shown in FIG. 2, because the strand surface is composed of copper, it is easier for the eddy current to flow near the strand surface, and heat is generated by the resistance of copper, adversely affecting the stability of the superconducting coil. Narrow strands are therefore used to reduce the eddy current loss. A design standard is given by Equation 1: EQU d&lt;.delta. (1)
where .delta. is the characteristic depth (penetration depth) of the skin effect, and d is the strand diameter. Such a narrow strand is well suited to being processed into a filament from NbTi or the like.
Another reason for twisting together several strands is that folding must be performed to obtain a cable that is to be used for coil formation. A failure to twist the strands will adversely affect bendability and will sometimes result in breakage. The coil being manufactured is commonly bent in a single direction. The coil will therefore have different lengths on in the inside and outside. If the strands were not twisted, they would be stretched on the outside and compressed on the inside. Stranding is performed in order to prevent any deterioration in the characteristics of a superconducting conductor based on such an asymmetric structure. A coil is fabricated by winding the CIC cables thus fabricated into a prescribed shape.
In order for stranding to minimize AC loss mentioned above, it is desirable to electrically insulate the strands from each other when an AC circuit or the like is used. The reason is that if the surfaces of a plurality of strands are electrically connected, the strands can be viewed as a single cable having a substantial surface area and volume, with the resulting increase in the eddy current loss W. The eddy current loss is proportional to the square of the characteristic strand diameter as given by the formula: EQU W.varies.d.sup.2 (2)
where W is the eddy current loss, and d is the characteristic strand diameter. In practice, even a single strand has a multitude of contact sites, so the eddy current flows in a complex manner.
In the experiments for demonstration poloidal coils (DPCs) by the Japan Atomic Energy Research Institute (JAERI), owing to the aforementioned reasons, various strands are insulated with formvar during the fabrication of NbTi-30 kA class coils (DPC-U) with CIC cables. Specifically, the insulator formvar is applied in a thickness of several micrometers to the surface of the strand shown in FIG. 2 (see FIG. 3). In other words, complete inter-strand insulation is ensured by the coating of the strand surface with the insulator as shown in FIG. 3. Thus a structure with individually insulated superconducting strands has been implemented in the DPC experiments in order to obtain a stabilized superconducting coil with a low AC loss (in addition to the eddy current loss, the losses sustained by superconducting coils used in AC circuits include the hysteresis loss, proximity effect, and the like, but the eddy current loss is usually predominant).
The original intent of the JAERI's DPC project was to establish a world record with respect to the rate of change of the magnetic field dB/dt, and to enable the coil to ultimately be quenched at a much lower rate of change of the magnetic field dB/dt than that employed for a conventional coil. In practice, however, the DPC experiments performed by JAERI did not go as planned. The results demonstrated that the value of the rate of change of the magnetic field dB/dt at which such a superconducting coil could operate stably was about 1/1000 of the initial design value before quenching sets in.
The rate of change of the magnetic filed is measured by using pulsed current waveforms (see FIG. 4) prior to the passage of an AC current. Because of the separate excitation of the coil, the magnetic waveform generated by the coil resembles that in FIG. 4. It is therefore possible to determine the rate of change of the magnetic field dB/dt (time derivative of the magnetic field) during the time 0 to t.sub.1. In the experiments, the time from 0 to t.sub.1 and the I.sub.0 value were controlled by an external power supply, and stability and other data concerning the superconducting coil were obtained by varying the rate of change of the magnetic field dB/dt.
The reasons for the disappointing DPC experiments were extensively researched by JAERI and by other scientific and manufacturing establishments, and it was discovered that it was due to the electric currents flowing through individual strands differed from each other and underwent significant channeling. The effect is that some strand will have more current bunched up in it and therefore exceed the critical current (i.e., current that demarcates between super- and normal-conducting states) more readily than others. This introduces instability to the overall cable system and initiates early quenching even though the average current in the strands is well below the critical current.
The following is an overall analysis of undesirable quenching due to current imbalance resulting from strands channeling.
FIG. 5 shows an equivalent circuit for a case in which two strands (for the sake of simplicity) are used. Strand 1 has self-inductance L.sub.1 and resistance R.sub.1, and strand 2 has L.sub.2 as the self-inductance and R.sub.2 the resistance, and M is the mutual inductance. The electrical network equations are given by Equations 3 and 4: EQU V=R.sub.1 .multidot.I.sub.1 +j.omega.L.sub.1 .multidot.*I.sub.1 +j.omega.M.multidot.I.sub.2 (3) EQU V=R.sub.2 .multidot.I.sub.2 +j.omega.L.sub.2 .multidot.*I.sub.2 +j.omega.M.multidot.I.sub.1 (4)
where .omega. is the oscillation frequency of the circuit, and j is an imaginary number such that j.sup.2 =-1.
Solving Equations 3 and 4 above for the currents I.sub.1 and I.sub.2 will yield Equation 5: EQU I.sub.1 /I.sub.2 =[R.sub.2 +j.omega.)(L.sub.2 -M)]/[R.sub.1 +j.omega.(L.sub.1 -M)]. (5)
Because the strands in question are in a superconducting state, it can be assumed that R.sub.1 =R.sub.2 =0 in Equation 5 above, in which case the current ratio of the two strands will be expressed by Equation 5' below. EQU I.sub.1 /I.sub.2 =(L.sub.2 -M)/(L.sub.1 -M) (5')
Two features lead to Equation 5' yielding greatly differing currents in two strands. One is that the mutual inductance M has a value that is very close to the self-impedance L.sub.1 or L.sub.2 because the strands have been wound closely to each other. The other is that the self-inductances L.sub.1 and L.sub.2 do not have identical values, but differ slightly from each other.
Measurement results obtained using JAERI's DPC indicate that self-inductance fluctuates by up to about 1% and that the mutual inductance is about 99% of the self-inductance. Substituting this result into Equation 5' above makes it possible to derive Equation 6 below. EQU I.sub.1 /I.sub.2 =(101-99)/(100"99)=2/1 (6)
It is thus concluded that even a slight difference in impedance can result in an inter-strand current ratio of 2.
On the other hand, when the current in a strand exceeds a fixed value, namely, the critical current I.sub.c, quenching will occur. With the unequal distribution of the current among the strands and the widely varying currents in the different strands, those strands bearing the higher current will exceed I.sub.c earlier than others. Specifically, quenching occurs in the aforementioned structure of JAERI's DPC when the current flowing through a number of strands (out of a total of 486 strands) exceeds I.sub.c. This causes the entire coil to be quenched, with the result that the stably flowing electric current corresponds to a mere 1/1000 of the originally intended rate of change of the magnetic field dB/dt.
This phenomenon is still being extensively analyzed and researched, and results of this research have already been published in a variety of sources, some of which are cited below.
Ando et al., "Analysis of Channeling in Cases of Contact Points in Superconducting Stranded Cables for Alternating Currents/Pulses [Denryu/Parusu Yo Chodendo Yorisen Dotai no Naibu ni Sesshokuten ga Aru Toki no Henryu no Kaisetsu]," Collected Preprints of 52.sup.nd Meeting of Low-Temperature Engineering/Superconductivity Society, Fall of 1994, E1-22, p. 229.
Koizumi et al., "Channeling Phenomena in 30 kA Class NbTi Cables [30 kA Kyu NbTi Dotai no Henryu Gensho]," Collected Preprints of 52.sup.nd Meeting of Low-Temperature Engineering/Superconductivity Society, Fall of 1994, A3-10, p. 229.
Hida at al., "Quenching Characteristics of Passage of Alternating Currents Through Superconducting Stranded Cables for Alternating-Current Applications [Koryu Yo Chodendo Yorisen Dotai in Okeru Koryu Tsudenji no Kuenchi Tokusei ni Tsuite]," Collected Preprints of 52.sup.nd Meeting of Low-Temperature Engineering/Superconductivity Society, Fall of 1994, A3-3, p. 222.
Of these, Koizumi et al. of JAERI indicated that, based on the coolant temperature dependence of the quenching current value, electric currents differing by as high as a factor of 7.1 of the average current value can flow through a plurality of strands. In addition, the disturbance of the self-inductance of a strand and the strand length have been estimated at 0.12% and 0.06%, respectively, in the case of a DPC-U cable.
One solution to reduce the uneven channeling of current among the strands is to relax the insulation of the strands. In this way, there will be some interstrand conduction that allows redistribution of the currents from one strand to others.
Based on the analysis results described above, recently manufactured CIC cables were chrome-plated rather than being insulated with formvar on the strand surface, as shown in FIG. 3. Because the strands are not completely insulated when the surfaces of these strands are chrome-plated, the eddy current loss increases, as was described in the beginning, but the loss is lower than in the case of a bare copper surface. This is because chromium has a lower electrical conductivity than copper.
Another mechanism for early quenching is when strand channeling causes the eddy current in some strands to exceed the critical current. Quenching commonly starts in portions containing such strands. Because voltage is generated by the resistance of the portion in which quenching was thus initiated, the electric current is reversed (that is, shunted) from the chrome-plated contact area to other elements.
FIG. 6 shows the manner in which the current is shunted by quenching in two strands. In FIG. 6, R.sub.1 is the resistance based on the quenching generated as a result of the fact that the critical current I.sub.c has been exceeded, and R.sub.c is the contact resistance of the chrome plating. The electric current I.sub.1 flowing through the strand 1 is shunted in the quench portion. The magnitude thereof is determined by the resistances R.sub.1 and R.sub.c, and the ratio of the current shunted to the strand 2 increases with an increase in the resistance R.sub.1. Thus, current redistribution increases with R.sub.1. In practice, this phenomenon involves numerous strands. Performing such shunting makes it possible for the strand current to be rendered uniform and for the coil to be operated stably.
Adopting such a structure, however, makes it necessary to examine the thickness of the chrome plating, the reversal of the eddy current in conformity with the thickness of the chrome plating, and the like, complicating the analysis and requiring experiments. Such studies are described, for example, in Takahashi et al., and Hida at al., and in the literature described below.
Tsuchioka et al., "Analysis of Channeling Between Strands in Cables [Keburu Dotai ni Okeru Sosenkan Henryu no Kaisetsu'," Collected Preprints of 52.sup.nd Meeting of Low-Temperature Engineering/Superconductivity Society, Fall of 1994, E1-24, p. 121.
Ultimately, the main conclusion of this research was the realization that it is of utmost importance in the design technique of a CIC cable that while total insulation is provided in order to reduce the eddy current loss, but in view of strand channeling, chrome plating and the like for reducing the insulation are adjusted in accordance with the required coil specifications.
A comprehensive design technique for adjusting the chrome plating or the like in accordance with the required coil specifications has yet to be established, however.
The present inventor, in Japanese Patent Application 6-316071, tried to address the aforementioned problems and proposed a superconducting cable system in which a plurality of lead wires that form current leads are connected to the corresponding superconducting strands without being bundled together, as shown in FIG. 7.
Coils are often fabricated in the form of double pancakes, and many such pancakes are connected into a single coil. The double pancake cables of a poloidal coil in a large helical device (LHD) called a large superconducting coil have a length of about 170 m. The maximum length that should be adjusted is therefore about 0.102 m, as given by the formula 170.times.0.06%=0.102 m.
Formation of pronounced channeling can therefore be avoided by adopting a structure in which the length of a strand measuring about 10 cm can be adjusted in the connection area of each double pancake.
In FIG. 7, strands of varying length are connected to individual superconducting strands, and all the strands are attached together to a connector terminal. The superconducting coil is in a low-temperature environment, and the power supply thereof is at normal temperature. Connections can be completed using highly electroconductive copper, aluminum, or the like, but Joule heat and conduction of heat from the normal-temperature environment to the low-temperature environment are difficult to analyze. Devices called "current leads" are therefore used.